A Novel Fully Interval-Valued Intuitionistic Fuzzy Multi-objective Indefinite Quadratic Transportation Problem with an Application to Cost and Wastage Management in the Food Industry

The framework of any transportation problem is structured on the basis of parameters like supply, demand, cost, and quantity. Nowadays, the tech-savvy consumers globally enjoy the ease and comfort of the so-called delivery apps which make these parameters uncertain and imprecise, and hence crisp parameters are unable to handle or represent such situations. The more flexible and generalized fuzzy number, namely, the interval-valued intuitionistic fuzzy number, can come handy to the decision-maker for efficient representation of all these parameters. However, the purpose of the decision-maker is not only to minimize the transportation cost while delivering the article of trade but also to minimize other associated costs. Many authors have worked with fully intuitionistic fuzzy multi-objective transportation problem with standard linear objective function with and without using interval-valued intuitionistic fuzzy numbers. This work proposes a comprehensive novel fully interval-valued intuitionistic fuzzy multi-objective indefinite quadratic transportation problem. Indefinite quadratic objective function being product of two linear factors is capable of minimizing each of the factors simultaneously. Authenticity of the model is exhibited through a real-life problem scripted from the food industry. The first objective minimizes the transportation cost and the depreciation cost simultaneously. In the second objective, simultaneous minimization of the packaging cost and the associated wastage cost is targeted. The problem is solved through a proposed and an existing methodology. The results obtained are discussed and future work concludes the chapter.